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1.8. Consider the following transition matrices. Identify the transient and recurrent states, and the irreducible closed sets in the Markov chains. Give reasons for your answers. (a) 1 2 3 4 5 1 2 3 4 5 4 .3 .3 00 0.5 0.5 0 .5 0.5 0 0 0.5 0.5 0 0.3 0.3 .4 2 (c) 1 2 3 4 5 1 00001 0.2 0.8 0 .1 .2 .4 .3 0 4 0.4 0.6 0 5.2 0 0 0.8 3 50.200.80 6 0.3 0.3 0.4 3 4 1 1 0 0 0 0 2/3 O 1/3 O 1/8 1/4 5/8 0 0 0 1/6 0 5/6 0 5 1/3 0 1/3 0 1/3 (e) 1 3 4 1 (b) 1 2 3 4 5 6 .1 0 0 .4 .5 0 2.1.2.2 0.5 0 30.1.3 0 0.6 4.10 0.900 5 0 0 0.4 0.6 6000 0.5.5 (d) 1 2 3 4 5 6 1 .8 0 0.20 0 2 0.50 0.5 0 3 0 0 .3 .4 .1 .2 4.10 0.900 2 0

1.8. Consider the following transition matrices. Identify the transient and recurrent states, and the irreducible closed sets in the Markov chains. Give reasons for your answers. (a) 1 2 3 4 5 1 2 3 4 5 4 .3 .3 00 0.5 0.5 0 .5 0.5 0 0 0.5 0.5 0 0.3 0.3 .4 2 (c) 1 2 3 4 5 1 00001 0.2 0.8 0 .1 .2 .4 .3 0 4 0.4 0.6 0 5.2 0 0 0.8 3 50.200.80 6 0.3 0.3 0.4 3 4 1 1 0 0 0 0 2/3 O 1/3 O 1/8 1/4 5/8 0 0 0 1/6 0 5/6 0 5 1/3 0 1/3 0 1/3 (e) 1 3 4 1 (b) 1 2 3 4 5 6 .1 0 0 .4 .5 0 2.1.2.2 0.5 0 30.1.3 0 0.6 4.10 0.900 5 0 0 0.4 0.6 6000 0.5.5 (d) 1 2 3 4 5 6 1 .8 0 0.20 0 2 0.50 0.5 0 3 0 0 .3 .4 .1 .2 4.10 0.900 2 0

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 49E: Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show...
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lay. 1.8. Consider the following transition matrices. Identify the transient and recurrent states, and the irreducible closed sets in the Markov chains. Give reasons for your answers. (a) 1 2 3 4 5 12345 .4 .3 .3 00 0.5 0 .5 O 0 3 .5 0.5 0 4 0.5 0.5 0 5 0.3 0 .3 .4 1 2 3 (c) 1 2 3 4 5 00001 0.2 0.8 0 .1 .2 .4 .3 0 4 0.4 0.6 0 5.2 0 0 0.8 1 6 0.3 0.3 0.4 3 4 5 1 0 0 0 0 2/3 0 1/3 0 1/8 1/4 5/8 0 0 0 1/6 O 5/6 0 5 1/3 0 1/3 0 1/3 (e) 1 2 3 4 (b) 1 2 3 456 1 .1 0 0 .4 .5 O 2 .1 .2.2 0.5 0 3 0.1.3 0 0.6 4.10 0.90 0 5 0 0 TO 4 0 6 6 000 0.5.5 (d) 1 2 3 4 5 6 1.8 0 0.20 0 20.50 0.5 0 3 0 0 .3 .4 .1 .2 4.10 0.90 0 50.200.80 2 0
Transcribed Image Text:lay. 1.8. Consider the following transition matrices. Identify the transient and recurrent states, and the irreducible closed sets in the Markov chains. Give reasons for your answers. (a) 1 2 3 4 5 12345 .4 .3 .3 00 0.5 0 .5 O 0 3 .5 0.5 0 4 0.5 0.5 0 5 0.3 0 .3 .4 1 2 3 (c) 1 2 3 4 5 00001 0.2 0.8 0 .1 .2 .4 .3 0 4 0.4 0.6 0 5.2 0 0 0.8 1 6 0.3 0.3 0.4 3 4 5 1 0 0 0 0 2/3 0 1/3 0 1/8 1/4 5/8 0 0 0 1/6 O 5/6 0 5 1/3 0 1/3 0 1/3 (e) 1 2 3 4 (b) 1 2 3 456 1 .1 0 0 .4 .5 O 2 .1 .2.2 0.5 0 3 0.1.3 0 0.6 4.10 0.90 0 5 0 0 TO 4 0 6 6 000 0.5.5 (d) 1 2 3 4 5 6 1.8 0 0.20 0 20.50 0.5 0 3 0 0 .3 .4 .1 .2 4.10 0.90 0 50.200.80 2 0
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